Here \(U_\perp \)  corresponds to the normalisations speed and \(\Gamma (z)\)  is the Gamma-function [1]}.
In both cases (RKD and SKD), for large \(E\)  the distribution function follow
a power law form in energy of \(\approx E^{-\kappa }\) . For energies \(E>E_0\)  we can approximate the \(\kappa \)  part of the RKD

j(E)  E-e-2EE0

(for the SKD without the exponential term). The exponential term approximates unity
as long as the argument is (much) less than one (\(\xi ^2 E/E_0 <1\) ).
